Nanoscale imaging of equilibrium quantum Hall edge currents and of the magnetic monopole response in graphene

Although the recently predicted topological magnetoelectric effect¹ and the response to an electric charge that mimics an induced mirror magnetic monopole² are fundamental attributes of topological states of matter with broken time-reversal symmetry, so far they have not been directly observed in experiments. Using a SQUID-on-tip³, acting simultaneously as a tunable scanning electric charge and as an ultrasensitive nanoscale magnetometer, we induce and directly image the microscopic currents generating the magnetic monopole response in a graphene quantum Hall electron system. We find a rich and complex nonlinear behaviour, governed by the coexistence of topological and non-topological equilibrium currents, that is not captured by the monopole models². Furthermore, by imaging the equilibrium currents of individual quantum Hall edge states, we reveal that the edge states, which are commonly assumed to carry only a chiral downstream current, in fact carry a pair of counterpropagating currents⁴, in which the topological downstream current in the incompressible region is counterbalanced by a non-topological upstream current flowing in the adjacent compressible region. The intricate patterns of the counterpropagating equilibrium-state orbital currents provide insights into the microscopic origins of the topological and non-topological charge and energy flow in quantum Hall systems.